Prelimit Coupling and Steady-State Convergence of Constant-Step-Size Nonsmooth Contractive Stochastic Approximation
A prelimit coupling framework for analyzing nonsmooth stochastic approximation procedures is developed, which establishes Wasserstein convergence to a unique stationary distribution, characterize the limiting steady-state distribution as the step size vanishes, and shows that nonsmoothness can create a bias of order of...